Q: What are the factor combinations of the number 304,108,291?

 A:
Positive:   1 x 30410829117 x 1788872337 x 821914373 x 4165867179 x 1698929629 x 4834791241 x 2450511369 x 2221392701 x 1125913043 x 999376623 x 4591713067 x 23273
Negative: -1 x -304108291-17 x -17888723-37 x -8219143-73 x -4165867-179 x -1698929-629 x -483479-1241 x -245051-1369 x -222139-2701 x -112591-3043 x -99937-6623 x -45917-13067 x -23273


How do I find the factor combinations of the number 304,108,291?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 304,108,291, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 304,108,291
-1 -304,108,291

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 304,108,291.

Example:
1 x 304,108,291 = 304,108,291
and
-1 x -304,108,291 = 304,108,291
Notice both answers equal 304,108,291

With that explanation out of the way, let's continue. Next, we take the number 304,108,291 and divide it by 2:

304,108,291 ÷ 2 = 152,054,145.5

If the quotient is a whole number, then 2 and 152,054,145.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 304,108,291
-1 -304,108,291

Now, we try dividing 304,108,291 by 3:

304,108,291 ÷ 3 = 101,369,430.3333

If the quotient is a whole number, then 3 and 101,369,430.3333 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 304,108,291
-1 -304,108,291

Let's try dividing by 4:

304,108,291 ÷ 4 = 76,027,072.75

If the quotient is a whole number, then 4 and 76,027,072.75 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 304,108,291
-1 304,108,291
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

11737731796291,2411,3692,7013,0436,62313,06723,27345,91799,937112,591222,139245,051483,4791,698,9294,165,8678,219,14317,888,723304,108,291
-1-17-37-73-179-629-1,241-1,369-2,701-3,043-6,623-13,067-23,273-45,917-99,937-112,591-222,139-245,051-483,479-1,698,929-4,165,867-8,219,143-17,888,723-304,108,291

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